{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ExtendedDefaultRules #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# OPTIONS_GHC -Wall #-}
{-# OPTIONS_GHC -fno-warn-type-defaults #-}

module Data.Mealy.Simulate
  ( rvs,
    rvsp,
    create,
  )
where

import Control.Monad.Primitive (PrimState)
import NumHask.Prelude hiding (fold)
import System.Random.MWC.Probability

-- $setup
-- >>> :set -XFlexibleContexts
-- >>> import Data.Mealy
-- >>> gen <- create
-- >>> let n = 3
-- >>> let eq' a b = all nearZero $ zipWith (-) a b
-- >>> let eq'p a b = all (\x -> x) $ zipWith (\(x0,x1) (y0,y1) -> nearZero (x0-y0) && nearZero (x1-y1)) a b

-- | rvs creates a list of standard normal random variates.
-- >>> t <- rvs gen n
-- >>> t `eq'` [-0.8077385934202513,-1.3423948150518445,-0.4900206084002882]
-- True
--
-- >>> rs <- rvs gen 10000
-- >>> fold (ma 1) rs
-- -1.735737734197327e-3
--
-- >>> fold (std 1) rs
-- 0.9923615647768976
rvs :: Gen (PrimState IO) -> Int -> IO [Double]
rvs :: Gen (PrimState IO) -> Int -> IO [Double]
rvs Gen (PrimState IO)
gen Int
n = Int -> Prob IO Double -> Gen (PrimState IO) -> IO [Double]
forall (m :: * -> *) a.
PrimMonad m =>
Int -> Prob m a -> Gen (PrimState m) -> m [a]
samples Int
n Prob IO Double
forall (m :: * -> *). PrimMonad m => Prob m Double
standardNormal Gen (PrimState IO)
gen

-- | rvsPair generates a list of correlated random variate tuples
-- |
-- >>> t <- rvsp gen 3 0.8
-- >>> t `eq'p` [(-0.8077385934202513,-1.4591410449385904),(-1.3423948150518445,-0.6046212701237168),(-0.4900206084002882,0.923007518547542)]
-- True
--
-- >>> rsp <- rvsp gen 10000 0.8
-- >>> fold (corr (ma 1) (std 1)) rsp
-- 0.7933213647252008
rvsp :: Gen (PrimState IO) -> Int -> Double -> IO [(Double, Double)]
rvsp :: Gen (PrimState IO) -> Int -> Double -> IO [(Double, Double)]
rvsp Gen (PrimState IO)
gen Int
n Double
c = do
  [Double]
s0 <- Gen (PrimState IO) -> Int -> IO [Double]
rvs Gen (PrimState IO)
gen Int
n
  [Double]
s1 <- Gen (PrimState IO) -> Int -> IO [Double]
rvs Gen (PrimState IO)
gen Int
n
  let s1' :: [Double]
s1' = (Double -> Double -> Double) -> [Double] -> [Double] -> [Double]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\Double
x Double
y -> Double
c Double -> Double -> Double
forall a. Multiplicative a => a -> a -> a
* Double
x Double -> Double -> Double
forall a. Additive a => a -> a -> a
+ Double -> Double
forall a. ExpField a => a -> a
sqrt (Double
1 Double -> Double -> Double
forall a. Subtractive a => a -> a -> a
- Double
c Double -> Double -> Double
forall a. Multiplicative a => a -> a -> a
* Double
c) Double -> Double -> Double
forall a. Multiplicative a => a -> a -> a
* Double
y) [Double]
s0 [Double]
s1
  [(Double, Double)] -> IO [(Double, Double)]
forall (f :: * -> *) a. Applicative f => a -> f a
pure ([(Double, Double)] -> IO [(Double, Double)])
-> [(Double, Double)] -> IO [(Double, Double)]
forall a b. (a -> b) -> a -> b
$ [Double] -> [Double] -> [(Double, Double)]
forall a b. [a] -> [b] -> [(a, b)]
zip [Double]
s0 [Double]
s1'